A numerical model for calculating photoacoustic signals from a blood vessel is presented based on the photoacoustic theory. With this model the influences of measurement parameters on photoacoustic signals and the accuracy of measurement of optical absorption coefficient of blood with the fitting-based pulsed photoacoustic method are demonstrated. The computational results indicate that the diameter of the blood vessel has a significant influence on the accuracy of the fitting-based pulsed photoacoustic method and it should be taken into account for improving the accuracy of this method.